Piezoelectric crystal apparatus



Mmh 31,1942. Mmmm Em, 2,277,709

PIEZOELECTRIC CRYSTAL APPARATUS Filed Dec. 12, 1940 2 Sh'lleets-Sheet l F IG.

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PIEZOELECTRIC CRYSTAL APPARATU S Filed Deo. 12, 1940 2 Sheets-Sheet 2 H. J msx/MN QLVENTORS- R. A. sy/Es w.. Q5. @mw

ATTORNEY Patented Mar. 31, 1942 PIEZOLECTRIC CRYSTAL .APPARATUS` v Herbert J. McSkimin, 'Lyndhurst4 and Roger A.

Sykes, Fanwootl, N. J., assignors to Bell Telephone Laboratories, Incorporated, Ncw York, N. Y., a corporation of New York Application December 12, 1940, Serial No. 369,694

(Cl. F11-327) Claims.

This invention relates to piezoelectric crystal apparatus and particularly to electroded piezoelectric quartz crystal elements suitable for use as circuit elements in electric wave filter systems, for example.

One of the objects of this invention is to Drovide a piezoelectric crystal element having aplurality of useful modes of motion that may be utilized simultaneously.

Another object of this invention is to Provide a crystal element having aplurality of independently controlled 'frequencies that are substantially uncoupled and free from spurious fre-l f quencies.

Another object of this invention is to reduce the number and the cost of crystals used in electric wave filter systems and other wave transmission networks.

Piezoelectric crystal elements generally c an be excited in many different modes of motion. When applied to filter systems for example, it is generally desirable to have all of the undesired or extraneous modes therein considerably higher, or lower, in frequency than the desired main mode or modes since .otherwise the extraneous resonance frequencies therein may introduce undesirable frequencies or pass bands in the lter characteristic. Accordingly, it is desirable that the two orY more separate desired main modes of motion of a crystal element be substantially uncoupled and independently controlled so that they may be given any desired frequency values to obtain a prescribedlter characteristic.

-In accordance with this invention, a Wave lter or other system may comprise as a component element thereof, a single piezoelectric crystal element adapted to vibrate simultaneously in a plurality of substantially uncoupled modes of motion in order to provide simultaneously a plurality of. useful effective lresonances which may be independently controlled and placed at pre determined frequencies of the same or diiferent values for use in an electric wave lter or elsewhere.

The crystal element may -be a, quartz crystal plate of suitable orientation andY dimensional proportions provided with a suitable electrode arrangement forsimultaneously driving two desired modes of motion and controlling the relative` strengths of the two resonances independently.

In a particular embodiment, the orientation of the crystal element may be that of an X-cut quartz crystal plate rotated in effect substantially -47 .5 degrees about its X-axis thickness dimension', and the ratio of the width dimension of its major surfaces with respect to the length dimensicn. thereof may be a value within the range from about 0.80 to 0.90 in order to obtain therefrom simultaneously two useful independently controlled resonant frequencies resulting from 6 two independently controlled modes of motion 0 crystal element of Fig. 8;

resonances is effective in the diagonal branch of Y the lattice portion of the equivalent network thereof, to obtain filter circuits using only a single crystal 'which are-'electrically equivalent to circuits requiring two crystals thereby reducing the number and cost of crystals therein. Suchl crystal elements may'be utilized for example in balanced or unbalanced filter structures.

For a clearer understanding of the nature of this invention and the additional advantages, features and objects thereof reference is made to the following description taken in connection with theaccompanying drawings, in which like reference Vcharacters represent like or similar parts and in which:

Fig. l is a majorface viewof a piezoelectric quartz crystal element in accordance wlthjthis invention and illustrates particularly the orientation thereof with'respect to the X, Y and Z axes of the natural crystal from whichit may be cut;

Figs. 2 and 3 are major face views of the crystal element of Fig. 1 illustrating in enlarged scale two types of motion which may be simultaneously utilized in crystal elements of the orientation illustrated in Fig. l, Fig. 2 illustrating the width dimension longitudinal mode of motion and Fig. 3 illustrating the double shear mode of motion: Fig. 4 is a graph illustrating the frequencies o'f the two independent modes of motion illustrated in Figs. 2 and 3 in crystal elements of the V Figs; 2 and 3 in order to'obtain the resonance frequencies given by the graphs of Fig. 4;

' Fig` 5 is a perspective view of the piezoelectric crystal element of Fig. 1 and associated electrodes therefor;

Fig. 6 is .a major face view of crystal element of'Fig. 5;

Fig. 7 is a schematic diagram illustrating'an example of balancediilter connections for the crystal element of Figs. 5 and 6;

Fig. 8 is a, perspective viewof a piezoelectric crystal element similar to that of Fig. 5 but illustrating another form of associated electrodes therefor;

Fig. 9 is a major face view ofthe electroded the electroded Fig. 10 is a schematic diagram illustrating an example of unbalanced iilter connections for the electroded crystal element of Fig. il;

Fig. 11 is a major face view of the crystal element of Fig. 1 similar to that of Fig, 6 but provided with another form of electrodes therefor; and

Fig. 12 is a schematic diagram illustrating a form of filter connections for the electroded crystal element of Fig. 11.

This specification follows the conventional terminology as applied to crystalline quartz which employs three orthogonal or mutually perpendicular X, Y and Z axes, as shown in the drawings, to designate an electric axis, a mechanical axis and the optic axis, respectively, of piezoelectric quartz crystal material, and which employs three orthogonal axes X', Y and Z to designate the directions of axes of a piezoelectric body angularly oriented with respect to such X, Y and Z axes thereof. Where the orientation is obtained by a single rotation of the quartz crystal element I, the rotation being in effect substantially about the thickness dimenw sion electric X of the piezoelectric body I, as il lustrated in Fig. 1, the orientation angle a=sub stantially 47.5 degreesdesignates in degrees the effective angular position of the crystal plate I as measured from the optic axis Z and from the mechanical axis Y.

Quartz crystals may occur in two forms, namely, right-handed and left-handed. A right.- handed quartz crystal is one in which the plane of polarization of a plane polarized light ray traveling along the optic axis Z in the crystal is rotated in a right-hand direction, or clockwise as viewed by an observer located at the light source and facing the crystal. This definition of right-handed quartz follows the convention which originated with Herschel. Trans. Cam. Phil. Soc. vol. 1, page 43 (1812); Nature vol. 110, page 807 (1922); Quartz Resonators and Oscillator`s, P. Vigoureux, page 12 (1931) Conversely, a quartz crystal is designated as left-handed if it rotates suchlplane of polarization referred to in the left-handed or counter-clockwise direction, namely, in the direction opposite to that given hereinbefore for the right-handed crystal.

If a compressional stress or a squeeze be ap plied to the ends of an electric axis X of a quartz body I and not removed, a charge will be developed which is positive at the positive end of the X axis and negative at the negative end of such electric axis X, for either right-handed or left'handed crystals. The magnitude and sign of the charge may be measured in a known manner with a vacuum tube electrcmeter, for exam--y ple. In specifying the orientation of a righthanded crystal, the sense of the angle a which negative orientation angle a with respect to the n Conversely, the orientation f" Y axis or the Z axis. angle of a left-handed crystal is positive when,

Iwith the compression positive end (+l of the electric axis X pointed toward the observer. the

. rotation is counter-clockwise, and is negative when the rotation is clockwise. The crystal matermi ulustratedin Fig. 1 is right-handed as the term is used herein. For ei-ther righthanded 0r tially minus 47.5 degrees.

amarte left-handed quartz, a position (-l-l angle a rotation of the Z axis with respect to the Z axis is toward parallelism with the plane oi' a minor apex face of the natural quartz crystal, and a negative (--.l a angle rotation of the Z axis with respect to the Z axis as illustrated in Fig. 1 is toward parallelism with the plane of a major apex face of the natural quartz crystal.

Referring to the drawings, Fig. l is a major face View of a thin piezoelectric quartz crystal clement I cut from crystal quartz free from twinning, veils or other inclusions and made into a plate of substantially rectangular parallelepiped shaped having a length or longest dimension L, a width dimension W which is perpendicular to the length dimension L, and a thickness or thin dimension T which is perpendicular to the other two dimensions L and W. In accordance with the values given by the curves of Fig. 4, the final width dimension W of the quartz crystal element I is determined by and may be made of a. value according to the desired longitudinal mode resonantfrequency. The width dimension W also may be related to the length dimension L in accordance with the Value of the dimensional ratio selected to obtain the desired double shear Inode resonant frequency. The thickness dlmension 'I' maybe of the order of l millimeter or anyother suitable value for example, to suit the impedance of the circuit in which the crystal element I may be utilized.

As shown in Fig. 1, the length dimension L of the crystal element I lies along a Y' axis in the plane of a mechanical axis Y and the optic axis Z of the quartz crystal material from which the element I is cut and is inclined at an angle of` a degrees with respect to said Y axis, the angle a being one of the values in the region of substan- The major surfaces 3 and 4 and the major plane of the bare quartz crystal element I are disposed parallel or nearly parallel with respect to the plane o! the Y and Z axes, the length dimension L and the width dimension W lying along the Y axis and the Z' axis, respectively, both of which lie` in the plane of the Y and Z axes'mentioned, the Y axis and the Z axis being inclined at the angle a with respect to the Y axis and the optic axis Z, respectively. The axis Z' is accordingly the result of a single rotation of the width dimension W about the X axis -a degrees. It will be noted that the crystal element I is in effect an X-cut quartz crystal plate rotated a degrees about the X axis.

Suitable conductive electrodes, such as the crystal electrodes of Figs. 5 to 1-2, for example,

may be placed on or adjacent to or formed in-v dimensions involving .the width dimension W and `the dimensional ratio of the width W with respect to the length L, the frequencies being values within a range roughly from about 340 to 360 kilocycles per second per centimeter of the width dimension W, as illustrated by the curves oi' The crystal electrodes when formed integral with the major surfaces 3 and I of the crystal element I may consist of thin coatings of silver, gold, platinum, aluminum or other suitable metal or metals deposited upon the bare quartz by evaporation in vacuum for example, or by other suitable process. When the quartz crystal plate I has an orientation angle of a=-47.5 degrees as illustrated in Fig. 1, the'S23 and S34 constants thereof are both of zero value. Accordingly, when the angle a is about 47.5 degrees, the Zz fundamental longitudinal or extensional mode along the width dimension W of the quartz plate I may be used simultaneously, and without'coupling to,.either (a) the second harmonic extensional mode along the Y' axis length dimension L involving the S23 constant, or (b) the double shear mode in the YZ plane of the crystal element I involving the S34 constant.

The principalmodes of interest that are particularly considered herein are the width longitudinal mode along the Z' axis, and the double shear mode in the Y'Z' plane of -they crystal element I, as illustrated in Figs. 2 and 3. More particularly, Figs. 2' and 3 are major face views of the quartz crystal element of Fig. 1 illustrating, in enlarged scale, the types of motion generated in the major plane Z'Y of the crystal element I for these two modes `of vibration of special interest.

Fig. 2 illustrates the width longitudinal or extensional mode of motion, and Fig. 3 illustrates the double shear mode of motion. In' Fig. 2, the broken lines and associated arrows indicate that the longitudinal width mode operates to alternately lengthen and shorten the width dimension W of the crystal element I about a nodal line 6 which extends across the center line Q length dimension L of the crystal element I. Similarly, in Fig. 3, the broken lines and associated small arrows indicate that the double shear mode operates to alternately extend and shorten the opposite corners and edges of the crystal element I about nodes 5 located at two points on the center line length dimension.L of the crystal element I.

It will be understood that the broken lines in Figs. 2 and 3 represent, in greatlyenlarged scale,

th general coniiguration of the edges of the c stal element I due to the lvibration of the crystal element I and are not intended to in.

vdicate the exact vibrational configuration of these edges but are merely illustrative representations of the types of motion involved in the width longitudinal mode and the double shear mode.

Since the nodes 5 involved in the double shear mode of motion of Fig. 3 are located onihe nodal line 6 involved in the width longitudinal mode of Fig. 3. Accordingly, at these nodal points 5,

the crystal element I may be mounted by rigidly clamping it between two pairs of oppositely disposed clamping projections-of small contact area which may be insertedin small indentations or depressions provided at the four nodal "points 5 oi' the crystal element I. Such small depressions cut in the major surfaces 3 and 4 of the crystal element I at the nodal points 5 thereof may have a depth of about 0.05 millimeter and a diameter of about 0.4 millimeter as measured on the survfaces 3 and l.

Fig. 4 is a graph illustrating the values of the resonance frequencies `associated. with the Width longitudinal mode and the dcuble'shear mode of Figs. 2 and 3, in a quartz crystal element I having an a angle of 47.5 degrees and having dimensional ratios of Width W with respect to length L in the region from about 0.83 to 0.91. The fundamental of the Z axis width W longitudinal mode frequency is represented by the two sections of the horizontal line curve A of Fig. 4 and has a frequency-dimension constant of about 351 kilocycles per second per centimeter of width dimension W independent of .the dimensional ratio of the width W with respect to the length L. The other mode of interest here-the socalled doubleshear mode-is represented by the two sections of the oblique line curve B of Fig. i and has a frequency constant of from 343 to 361 kilocycles per second per centimeter of width dimension W dependent upon the value of the selected dimensional ratio of width W with respect to length L within the range from about 0.83 to 0.90. The frequencies of these two modes of motion, as shown by the curves A and B of Fig. 4, approach each other when the ratioof the Z' axis width dimension W with respect to the Y' axis length dimension L is in the region-of about 0.86. In this region of special interest, theresonances of these two modes are substantially uncoupled or only very loosely coupled as is to be' expected since the S34 is equal to zero when the a angle of the quartz crystal element I has a value of -47.5"degrees as illustrated in Fig. 1. Accordingly, as shown in Fig. 4, when the dimensional ratio of W/L is in the region of 0.86

the frequencies of these two independent modes of vibration are close together but sufficiently uncoupled to provide simultaneously twoindependent frequencies from the same crystal element I, which may'be usefully employed ina filter system for example, to give conveniently frequencies of the order of toY 200 kilocycles per second for example within' a range of frequencies from 100 or less to 500 or more kilocycles per second.

The frequency in kilocycles per second of the longitudinal width mode vibrationfis the relation:

.fiarsags where W is the length of the width dimension W of the crystal element lI along the Z' axis ex-` This'v frequency relation pressed in centimeters. is illustrated by the two sections of vthe-horizontal line curve A of Fig. 4, and the type of motion there involved is illustrated in Fig. 2.

The frequency in kilocycles per second of the double shear lmode vibration is given by the relation lwhere L and W are respectively the length dimension L and the width dimension W of the crystal plate I expressed in centimeters, and where k is a function offfe coupling and proximity of iiexure modesfand in this caseghas a value of approximately 0.931.rv This-frequency given by relation is illustrated by the two sections of the oblique curve B of Fig. 4, and the type of motion involved therein is illustrated in Fig. 3.

The temperature coefficients of both the double shear mode frequency and the width W longitudinal mode frequency are negative, and are respectively of the order of about 23 and 49 parts per million per degree centigrade.

The principal extraneous frequencies which may occur in such crystal elements I are about 12 per cent away from the two desired main modes of motion described.

Figs. to .l2 illustrate several forms of electrode and connection arrangements which may be utilized to drive the crystal elements I of Fig. 1 simultaneously in the desired width longitudinal mode and the desired double shearmode illustrated in Figs. 2 and 3 respectively, in order to obtain smultaneously therefrom two independent resonance frequencies of values as given by the Y curves A and B of Fig. 4. As shown in Figs. 5 to 12, the desired double shear mode of motion may be driven by means of divided electrodes placed on one major surface only or on both of the major surfaces 3 and 4 of the crystal element I, while the desired longitudinal width mode may be driven at the same time by one of the connected sets of electrode platings, with the result that the two desired resonance frequencies of the crystal element I may be made to appear simultaneously.

As illustrated in Figs. 5 and 6, the quartz crystal element I of Fig. 1 may be provided with four equal-area electrodes IIl to I3, `two of the electrodes ID and II being placed on one major surface 4of the crystal element I with a narrow transverse split or gap or dividing line labeled 'I therebetween, and the other two electrodes I2 and I3, being oppositely disposed and placed on the opposite major surface 3 of the crystal element I and separated with a similar narrow and oppositely disposed split or dividing line I therebetween, the dividing lines I preferably extending generally in the direction of the Y axis of the crystal element I, according to the value of the 0 `angle selected, 0 being the angle between the direction of the dividing line 1 and the direction oi' the Y- axis length dimension L.

The gap or separation line 'I between the electrode platings on each of the major surfaces 3 i and 4 of the crystal element I may be of the order oi' about 0.3 millimeter, with the center line of such splits in the platings on the opposite sides I and 4 of the crystal plate I being aligned with v respect to each other.

Fig. 7 is a. schematic diagram illustrating an example of balanced filter connections which may be used with the electroded crystal elements I of Figs. 5 and 6 in order to obtain a lter systern comprising a single crystal element I having two independent simultaneously effective resonances which may be placed at any desired frequencies, one of which may appear in the line branch of the equivalent lattice and the other inA the diagonal branch thereof.

The balanced circuit of Figs. 5 to 7 may be converted into an unbalanced .filter structure by interconnecting the two electrodes I2 and I3 on one oi' the maior surfaces 3 of the crystal element I.`

In this case, the two electrodes I2 and I3 of Figs. 5 to 7 may be replaced by a single electrode I5 as shown in Fig. 8, and the electroded crystal element I of Figs. 8 vand 9 may be vconnected as shown schematically DLFIE. 10.

As illustrated in Figs. 8 to 10, to reduce the magnitude of the shunting capacitance appearing in the linebranch of the lattice lportion, a narrow grounding strip I4 of metallic plating maybe placed on one major surface 4 of the crystal element I between the electrodes IU and I I and may extend around one edge of the crystal element I to the opposite major surface 3 thereof where it may be electrically connected to the large electrode I5, as illustrated in Figs. 8 to l0. As illustrated in Figs. 8 to 10, the ground strip I4 of "metallic plating may be approximately I millimeter in width and may be placed between and separated from the two electrodes on the same major surface of the crystal eelment I in order to provide shielding and to reduce stray capacities to a minimum. The strip of plating I4 may extend from one major surface continuously over and around one edge only or both edges of the crystal plate I to the opposite major face thereof where it may make contact with the integral electrode on that surface.

It will be noted that in order to drive the crystal element I in the double shear mode, one half of the crystal plate is made of opposite polarity to that of the other half, as indicated by the -I- and signs in Fig. 9, and that this may be accomplished by utilizing a crystal element I having divided metallic coatings IIl and II placed on one of its major surfaces and connected in 'the form of a T network, for example, asI illustrated in Fig. 10. Inductance coils may be added in the usual manner in series or in parallel with the network of Fig. 10 to produce broad band low or high impedance filters for example.

' It will be noted that Fig. 10 is a schematic diagram illustrating an example of connections that may be utilized for connecting the electroded doubly resonant crystal element I of Figs. 8 and 9 in a filter system. In order that the crystal impedance may appear in both arms of the lattice structure of Fig. 10, one mode is driven when the terminals 2I and 23 are both of the same polarity, and the other mode is driven when these terminals 2I and 23 are of opposite polarity.

, Since both modes are substantially uncoupled or only loosely coupled mechanically, they may produce simultaneously two independent resonances half thereof. This may be done by adjustment l of the position of the electrode dividing line angle 0 with respect to the length dimension L. The angle 0 may be any desired value over a wide range of angles. This adjustment does not materially affect the impedance of the longitudinal width mode resonance, but with decreasing values for the angle 6 will increase the impedance level of the double shear mode resonance, without materially affecting the impedance of thewidth longitudinal mode resonance.

Thus, by changing the angle of inclination of the split or division line 1 between the electrodes I0 and II with respect tothe Y axis length dimension L of the crystal element, as illustrated by the angle 0 in Figs, 5, 6, 8, 9, 11, the internal capacity associated with the double shear mode, which is nearly a maximum value when 0 equals degrees, may be varied andadjusted to a desired value without changing the internal capacity Aassociated with longitudinal width mode.

desired ratio of internal capacities.

- tion:

Also, by scraping E: or otherwise removing a small amount of the electrode coating in the regions indicated-at I in Figs. 5 to 11, precise ad- Just-.ments in the internal capacity may be made. While there is an appreciable variation of the relative capacities with the 0 angle position of Ithe dividing line l between-the electrodes for example, for any given angle of between 45 and 120 degrees, the ratio of internal capacities is not iniluenced to any appreciable degree by a change in dimensional ratio of the width W with respect to the length L between the limits of about 0.87 and 0.89 for example which represents a useful range as indicated by the graph of Fig. 4. The dividing line 'l between the electrodesis preferably placed in the general direction toward parallelism with the Y axis of the crystal plate I, as illustrated in Figs. 5 to 11.

`Figs. l1v and 12 illustrate another form of electrode and connection arrangement which may be utilized to drive the crystal element I simultaneously in thetwo desired modes o'f virelatively small capacities are required to suit a particular circuit, the crystal element I may become inconveniently or excessively thickin the thickness direction dimension T. In this event, a relatively thin crystaleiement I may still be used with its metallic platings split as illustrated in Figs. 1l and 1,2. In this arrangement of crystal platings, effectively one-fourth of the crystal y element I is placed in series with another fourth, thus making one-eighth the total internal capacity appear in the lattice network. As illustrated. in Figs. 11 and ,12, the areas of the four platings IDA, IDB, IIC and IID on one face of the crystal y element I may allY be made of equal area, regardless of the angle 0 selected for the proper or The angle of Fig. 11 which'satisfles this condition of equali area platings IIlA, IDB, IIC and IID and also of the oppositely disposed equal-area electrodes IZA", IZB', I3C' and 13D' is [givenA by the rela- 2 i =tsn-1[%tan i-cot o] where is the angle between the direction of the.. Z' axis width dimension lW andthe direction of the separation lines 8 of the electrodes IIIA and IBB, IIIA' and IIIB', IIC and IID, IIC' and IID';

where 0, W and L have the lsigniiicance hereinbefore described.

As anv example, the quartz crystal element I may have length L, width' W and thickness T dimensions respectively of 34.64. 31.l2and 0.75

- millimeter with plating 'angles of q=51 degrees' and 4 =67 degrees to obtain a frequency in cycles vper second, of 115,857 for the double shear mode and 112,595 for the width longitudinal mode.

Connections between the electrode platings of Fig. l1 are illustrated schematically in Fig. 12 and may be made on the crystal element I itself by extending the integral metallic vplantings over and around two edges only of the crystal element I, thus leaving the other two edges thereof free y of plating for adjustment purposes.

It will be understood that Figs. 7,'10 and 12 represent particular circuits. In these and other forms of filter circuits, the doubly resonant crystal element I may be utilized. If desired, mutual clamping'form of mounting is used, two pairs of opposite conductive clamping projections may resiliently contact the electroded crystal element I at its four nodal points 5 only in order to support and to establish individual electrical connections therewith.

Alternatively,` instead of being mounted by clamping theelectroded crystal plate I may be mounted and electrically connected by soldering, cementing or otherwise firmly attaching four iine conductive supporting Wires directly 'to a thickened part of the electrodes of the crystal element I at its four nodal points 5 only. The four fine supporting wires referred to may be conveniently soldered to four small spots of baked silver paste orv other metallic paste, which have been previously applied at the nodal points 5 on the bare quartz underneath the iield producing crystal electrodes, whichmay consist of pure silver applied by the known evaporation in vacuum process. -Such iine supporting'wires secured tothe electroded crystal element I may extend horizontally from the ver-V -tical major surfaces of the crystal element I and at their other ends be attached 'by solder, for

example, to four vertical conductive wires or rods carried by the press or other part of .an evacuated or sealed glass or metal tube. The supporting wires and rods may have one or more bends therein to resiliently absorb mechanical vibrations. Also, bumpers or stops of softresilient material such as mica may be spaced closely adjacent the edges, ends or other parts of the electroded crystal element I in order to limit the' bodily displacement thereof when the device is subjected to mechanical shock. It will be understoodthat anyA holder which will give stability,

substantial freedom from spurious frequencies y Although this invention has been described and' illustrated in 4relation to specific arrangements,

' it is to be understood that itis capable of `appli- V cation in other organizations and is therefore not to be limited to the particularembodiments A disclosed, but only by the sco'pe of the appended claims Aand the state of the prior art. What is claimed is: l f l. A piezoelectricquartz crystal element having its substantially rectangular major surfaces sub-` stantially in the plane of a Y axis and the Z axis, the major axis lengthk dimension of rsaid major surfaces being inclined at an ang-le of substantially 47.5 degrees with respect to said Y axis, the dimensional ratio of the widthdimension of said major surfaces with respect to said length dimension thereof being one of the Avalues between substantially 0.80 and 0.93. .l

A piezoelectric quartz crystal element having its substantially rectangular major surfaces substantially in the plane of a Y axis and the Z axis, the major axis length dimension of said major surfaces being inclined at an angle of substantially 47.5 degrees with respect to said Y axis, the dimensional ratio of the width dimension of said major surfaces with respect to said length dimension thereof being one of the values between substantially 0.80 and 0.93, and means including electrodes adjacent said major surfaces for operating said element simultaneously at a plurality of independent frequencies dependent upon different sets of said major face dimensions.

3. A piezoelectric quartz crystal element having its substantially rectangular major surfaces substantially in the Diane of a Y axis and the Z axis, the major axis length dimension of said major surfaces being inclined at an angle of substantially 47.5 'degrees with respect to said Y axis, the dimensional ratio of the Width dimension of said major surfaces with respect to said length dimension thereof being one of the values between substantially 0.80 and 0.93, and means including electrodes adjacent said major surfaces for operating said element simultaneously at a plurality of independent frequencies dependent upon'said major face dimensions, one of said frequencies being dependent upon the fundamental of the longitudinalor extensional mode vibration along said width dimension.

4. A piezoelectric quartz crystal element hav- Y ing its substantially rectangular major surfaces substantially in the plane of a Y axis and the Z axis, the major axis length dimension of said major surfaces being inclined atan'angle of substantially 47.5 degrees with respect to said Y axis, the dimensional ratio of the Width dimension of said major surfaces with respect to said length dimension thereof being one of the values between substantially 0.80 and 0.93, and means including electrodes adjacent said major surfaces for operating said element simultaneously ata plurality of independent frequencies dependent upon said major face dimensions, one of said frequencies being dependent upon the fundamental of the longitudinal or extensional mode vibration along said width dimension, vand another of said frequencies being dependent upon the double shear mode vibration in said ZY plane.

A piezoelectric quartz crystal element adapte to vibrate simultaneously at a plurality of d ired independent frequencies dependent mainly upon the length and width dimensions of its substantially rectangular major surfaces, said length dimension being substantially in the plane' the ratio of said width dimension of said major' surfaces with respect to said length dimension thereof being one of the values within the region of substantially 0.86.

6. A piezoelectric quartz crystal element adapted to vibrate simultaneously at a plurality of de# lired independent frequencies dependent mainly upon the length and width dimensions of its substantially rectangular major surfaces, said length dimension being substantially in the plane of a Y axis and the Z axis and inclined at an angle of substantially 47.5 degrees with respect to said Y axis, said major surfaces being substantially parallel with-respect to said YZ plane, the ratio of the 4width dimension of said major -ed to vibrate simultaneously at a plurality of independent frequencies dependent mainly upon the length and widthdimensions of its substantially rectangular major surfaces, said length dimension being substantially in the plane of a Yaxis and the Z axis and inclined at an angle of substantially 47.5 degrees with respect to said Y axis, said major surfaces being substantially parallel with respect to said YZ plane, the ratio of the width dimension of said major surfaces with respect to said length dimension thereof being one of the values within the range from substantially 0.80 to 0.93, said'width dimension and said dimensional ratio being a set of corresponding values as determined by the curves of Fig. 4.

8. A piezoelectric quartz crystal element adapted t'i vibrate simultaneously at a plurality of desired frequencies dependent mainly upon the length and width dimensions of its substantially rectangular major surfaces, said length dimen sion being substantially inthe plane of a Y axis and the Z axis and inclined at an angle of substantially 47.5 degrees with respect to said Y axis, said major surfaces being substantially parallel with respect to said YZ plane, the ratio -of the width dimension of said major surfaces with respect to said length dimension thereof being one of the values within the range from substantially 0.83 to 0.90, said width dimension expressed in centimeters being a Value within the range. from substantially 340 to 360 divided by one of said frequencies expressed in kilocycles per second, said width dimension and said dimensional ratio being a set of values as given by the curves of Fig. 4. l

9. A piezoelectric quartz crystal element an means including two pairs of opposite electrodes adapted to vibrate said element simultaneously at a plurality of desired frequencies dependent mainly upon the length and width dimensions of the major surfaces of said element, said length dimension being substantially in the plane of a Y axis and the Z axis and disposed at an angle of 47.5 degrees with respect to said Y axis, said major surfaces being substantially parallel with respect to said YZ'plane.

10. A quartzv piezoelectric crystal element adapted izo-vibrate simultaneously at a plurality of desired frequencies dependent mainly upon the length and width dimensions of its major surfaces, said length dimension being substantially in the plane of a Y axis and the Z axis and inclined at an angle of substantially 47.5 degrees with respect to said Y axis, and said major surfaces being substantially parallel with respec-t to 'said YZ plane, two electrodes formed integral with one of said major surfaces, said 'electroded crystal element having nodes, said nodes being along the center line of said length dimension at points located from the ends thereof a distance substantially 0.25 of said length dimension.

HERBERT J. MCSKIMIN. ROGER A. SYKES. 

